# Bilateral Filter: Graph Spectral Interpretation and Extensions

arXiv: https://arxiv.org/abs/1303.2685 · HTML: https://mlsanity.com/paper/1303.2685/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2013.

## Built on by (most cited first, 8 of 8)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Graph Signal Restoration Using Nested Deep Algorithm Unrolling](https://mlsanity.com/paper/2106.15910/) (2021)
- [Volumetric 3D Point Cloud Attribute Compression: Learned polynomial bilateral filter for prediction](https://mlsanity.com/paper/2311.13533/) (2023)
- [Learned Nonlinear Predictor for Critically Sampled 3D Point Cloud Attribute Compression](https://mlsanity.com/paper/2311.13539/) (2023)
- [Graph Neural Network Surrogates of Fair Graph Filtering](https://mlsanity.com/paper/2303.08157/) (2023)
- [GACAN: Graph Attention-Convolution-Attention Networks for Traffic Forecasting Based on Multi-granularity Time Series](https://mlsanity.com/paper/2110.14331/) (2021)
- [Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer](https://mlsanity.com/paper/2409.06676/) (2024)
- [Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming](https://mlsanity.com/paper/2506.01826/) (2025)

## Abstract (arXiv)

In this paper we study the bilateral filter proposed by Tomasi and Manduchi, as a spectral domain transform defined on a weighted graph. The nodes of this graph represent the pixels in the image and a graph signal defined on the nodes represents the intensity values. Edge weights in the graph correspond to the bilateral filter coefficients and hence are data adaptive. Spectrum of a graph is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian matrix. We use this spectral interpretation to generalize the bilateral filter and propose more flexible and application specific spectral designs of bilateral-like filters. We show that these spectral filters can be implemented with k-iterative bilateral filtering operations and do not require expensive diagonalization of the Laplacian matrix.